Is it possible to give, not trade, a Pokémon to another player?
Solution 1:
No, Pokémon must be traded one-to-one, not given. I don't believe there has ever been an option to simply give Pokémon to someone else.
Tell your friends to catch a bunch of low-level Pokémon from the wild, which you can then release when they're traded to you.
Solution 2:
Yes. It is possible, however, you'll need to download Pokemon Bank, and insert your friend's game into your console.